One current educational reform seeks to reward the “value added” by teachers and schools based on the average change in pupil test scores over time. In this paper, we outline the conditions under which the average change in scores is sufficient to rank schools in terms of value added. A key condition is that socioeconomic outcomes be a linear function of test scores. Absent this condition, one can still derive the optimal value-added policy if one knows the relationship between test scores and socioeconomic outcomes, and the distribution of test scores both before and after the intervention.
Using the National Longitudinal Survey of Youth, we find a nonlinear relationship between test scores and one important outcome: log wages. We find no consistent pattern in the curvature of log wage returns to test scores (whether percentiles, scaled, or raw scores). This implies that, used alone, the average gain in test scores is an inadequate measure of school performance and current value-added methodology may misdirect school resources.